Active enable strong but sparse inputs to determine orientation selectivity

Lea Goetza, Arnd Rotha, and Michael Häussera,1

aWolfson Institute for Biomedical Research, University College London, London WC1E 6BT, United Kingdom

Edited by Tobias Bonhoeffer, Max Planck Institute of Neurobiology, , Germany, and approved June 9, 2021 (received for review August 16, 2020) The dendrites of neocortical pyramidal are excitable. How- trigger dendritic Na+ spikes and NMDA spikes. We also provide ever, it is unknown how synaptic inputs engage nonlinear dendritic a quantitative explanation for how these dendritic spikes determine mechanisms during sensory processing in vivo, and how they in turn neuronal output in vivo. Our results show that dendritic spikes can influence output. Here, we provide a quantitative be triggered by a surprisingly small number of synaptic inputs—in account of the relationship between synaptic inputs, nonlinear den- some cases even by single synapses. We also find that during sensory dritic events, and action potential output. We developed a detailed processing, already few dendritic spikes are effective at driving pyramidal model constrained by in vivo dendritic recordings. somatic output. Overall, this strategy allows a remarkably small We drive this model with realistic input patterns constrained by sensory number of strong synaptic inputs to dominate neural output, responses measured in vivo and connectivity measured in vitro. We which may reduce the number of neurons required to represent a show mechanistically that under realistic conditions, dendritic Na+ and given sensory feature. NMDA spikes are the major determinants of neuronal output in vivo. We demonstrate that these dendritic spikes can be triggered by a Results surprisingly small number of strong synaptic inputs, in some cases An Active Dendritic Model Reproduces Responses to Visual Stimulation. even by single synapses. We predict that dendritic excitability al- To study the mechanisms of synaptic integration during visual lows the 1% strongest synaptic inputs of a neuron to control the stimulation in vivo, we built and combined models of the sensory- tuning of its output. Active dendrites therefore allow smaller sub- evoked synaptic input and the postsynaptic pyramidal neuron circuits consisting of only a few strongly connected neurons to (Fig. 1 A and B; Materials and Methods). The postsynaptic model achieve selectivity for specific sensory features.

satisfies a large set of experimental constraints obtained in vitro NEUROSCIENCE (22, 23) and in vivo (21, 23, 24) (SI Appendix, Fig. S1). In par- | | synaptic integration | visual cortex | ticular, we constrained dendritic excitability and membrane po- dendritic spike tential dynamics during sensory processing by taking advantage of direct patch-clamp recordings from the dendrites of L2/3 py- here is longstanding evidence from in vitro experiments that ramidal neurons in mouse V1 in vivo (17). Tdendrites of mammalian neurons are electrically excitable (1, 2), The synaptic input model (SI Appendix,Fig.S2) satisfies con- and theoretical work has demonstrated that these active properties straints set by the experimentally measured distribution of firing can be exploited for computations so that single neurons can rates of the presynaptic neuron population (17), the overall number perform functions that could otherwise only be performed by a of synaptic inputs to the neuron (25), the mean number of synaptic network (3–7). Recently, technical breakthroughs have enabled contacts per connection (2.8) (19), and the connection probability dendritic integration to be studied in vivo using both imaging (26) and strength (18) as a function of the difference in orientation and electrophysiological techniques (8, 9). These experiments preference of the pre- and postsynaptic neurons (Materials and have revealed that the integration of synaptic events in vivo can Methods). A key assumption of the synaptic input model is the be highly nonlinear and that this process influences the response properties of single neurons and neuronal populations in vivo Significance (10–16). For example, patch-clamp recordings from dendrites in mouse primary visual cortex (V1) have demonstrated that dendritic An active pyramidal cell model, constrained by physiological and spikes are triggered by visual input and that they may contribute anatomical data, was used to simulate dendritic integration in to the orientation selectivity of somatic membrane potential (17). vivo. The model shows that small numbers of strong excitatory However, important mechanistic questions are still unanswered. synapses can trigger dendritic Na+ and NMDA spikes. Moreover, How many synaptic inputs must be locally coactive on a dendrite only a few dendritic spikes are sufficient to drive a single output to recruit dendritic spikes? What is the contribution of individual action potential. As a consequence, as few as 1% of the synaptic dendritic spikes to somatic action potential (AP) output and its inputs to a neuron can determine the tuning of somatic output orientation selectivity? Moreover, we do not understand how the in vivo. These results suggest that dendritic spikes can help to answers to these questions depend on the type of dendritic spike. make sensory representations more efficient and flexible: they Finally, how do active dendrites, by supporting dendritic spikes, require fewer connections to sustain them, and only a small influence which synaptic inputs control AP output and its tuning? number of connections need to be changed to encode a different These issues are extremely challenging to address experimen- stimulus and alter the response properties of a neuron. tally. We have therefore taken a modeling approach, constrained by in vitro and in vivo experimental data, in order to provide a Author contributions: L.G., A.R., and M.H. designed research; L.G. and A.R. performed quantitative understanding of the relationship between synaptic research; L.G. and A.R. analyzed data; and L.G., A.R., and M.H. wrote the paper. input, dendritic spikes, and AP output during sensory processing The authors declare no competing interest. inV1.Weconstructedadetailedactivemodelofalayer(L)2/3 This article is a PNAS Direct Submission. pyramidal neuron in mouse V1 and combined this with a model of This open access article is distributed under Creative Commons Attribution-NonCommercial- the presynaptic inputs it receives during visual stimulation with NoDerivatives License 4.0 (CC BY-NC-ND). drifting gratings in vivo (17–21). 1To whom correspondence may be addressed. Email: [email protected]. Our model reproduces key features of the experimental data This article contains supporting information online at https://www.pnas.org/lookup/suppl/ on dendritic and somatic responses to visual stimulation as ob- doi:10.1073/pnas.2017339118/-/DCSupplemental. served in vivo and allows us to identify the synaptic inputs that Published July 23, 2021.

PNAS 2021 Vol. 118 No. 30 e2017339118 https://doi.org/10.1073/pnas.2017339118 | 1of12 Downloaded by guest on October 1, 2021 ABsoma dendrite 0º

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20 mV 200 ms 75 μm 75 μm 86 μm 88 μm 88 μm Fig. 1. A pyramidal cell model with active dendrites reproduces dendritic responses to visual stimulation D in vivo. (A) Morphology of the L2/3 pyramidal neu-

) ron used for the model, with pipettes indicating the -1 locations of the recordings shown in B.(B) Example of somatic (Left) and dendritic (light blue, Right) )

-1 responses of the postsynaptic model neuron to sim- ulated synaptic inputs corresponding to visual stimuli with orientations 0°, 45°, 90°, and 135°, where 90° is the preferred orientation of the model neuron. (C) Comparison of dendritic patch-clamp recordings in vivo [pink, Left; data from Smith et al. (17)] with dendritic recordings in the model neuron (light blue,

Mean event rate (s Right). Note that vertical scale bars differ between traces. (D) Comparison of event rates in the experi- ment [pink; using data from Smith et al. (17)] and Max instantaneous event rate (s Variance to mean ratio (Fano factor) Variance model (light blue). Events are defined as episodes of monotonically rising membrane potential with a soma dendrite soma dendrite soma dendrite baseline-to-peak difference of more than 10 mV.

lognormal distribution of synaptic weights, which is supported events, as well as the variance-to-mean ratio (Fano factor) of the by experimental studies (27–31) reporting a small number of rel- distribution of event counts in a given time interval, were within atively strong connections among many weaker ones. Since no the same range in model and experiment (Fig. 1D). direct and complete recordings of the synaptic input received by a L2/3 neuron in vivo are available, and there is conflicting evidence Biophysical Definition of Dendritic Na+ Spikes and NMDA Spikes. regarding the spatial and temporal structure of active synapses Identifying and discriminating different types of active den- (32–37), we chose an approach in which different synaptic inputs dritic events is difficult in experimental dendritic recordings, are activated independently of each other so that any spatial or especially in vivo where it has not yet been possible to record temporal clustering occurs by chance.Wealsotestedanalternative dendritic and somatic voltages simultaneously. This means that synaptic input model in which synaptic inputs with similar tuning the signals arising from synaptic inputs, locally generated den- are spatially clustered. dritic spikes and backpropagating APs (bAPs), are difficult to The combined model reproduced somatic and dendritic re- separate. In the model, the ability to accurately track all of the sponses to visual stimulation in vivo, including their orientation relevant variables, namely synaptic currents, membrane poten- tuning (17) (Fig. 1B). In particular, the model exhibited a range tials, and the activation state of voltage-gated conductances, of dendritic spikes and plateau potentials at different dendritic allowed us to develop detectors for dendritic Na+ spikes, NMDA locations, which closely resembled the visually evoked events spikes, and bAPs based on a rigorous biophysical definition of observed in experimental dendritic recordings (Fig. 1C). Using individual events (reference SI Appendix). the same definition of events (SI Appendix, Fig. S3), the maxi- We detected local dendritic Na+ spikes using a conductance mum instantaneous and mean rates of somatic and dendritic density threshold of 0.3 mS/cm2. To validate this threshold, we

2of12 | PNAS Goetz et al. https://doi.org/10.1073/pnas.2017339118 Active dendrites enable strong but sparse inputs to determine orientation selectivity Downloaded by guest on October 1, 2021 compared simulations in our fully active model and a model in and a charge threshold of –0.1 nA ms. For NMDA spike de- which dendritic Nav conductances were switched off (38) (Fig. 2A, tection, both the current and voltage criteria have to be met within SI Appendix,Fig.S4,andMaterials and Methods). We defined aspatialwindowof±50 μm. We verified these criteria using fully dendritic Na+ spikes by an increase in local dendritic event am- active simulations and simulations in which NMDA conductances plitude of >10% from passive to active, which was well predicted were frozen at their resting potential (38) (Fig. 2B). 2 by a local dendritic gNa of more than 0.3 mS/cm (SI Appendix,Fig. S4C). Notably, actively backpropagating APs can also reach this Multiple Dendritic Na+ Spikes and NMDA Spikes Are Initiated Near conductance threshold. To prevent erroneous classification of Simultaneously across the Dendritic Tree. The relationship between bAPs as local Na+ spikes, we first identified a characteristic spa- dendritic spike initiation and the output of the neuron under in vivo tiotemporal bAP profile (latency and halfwidth) for each den- conditions is unknown and is critical for defining the input–output drite. Any dendritic event detected following a recent somatic function of the neuron. Our simulations allow us to provide a AP and matching the bAP profile for that dendrite was then quantitative account of this transformation, as we can track the classified as a bAP, rather than as a locally generated Na+ spike. initiation and propagation of all dendritic spikes and their rela- We detected dendritic NMDA spikes using both a voltage cri- tionship with output APs in the . Fig. 3A shows membrane terion and an NMDA current criterion, scaled by synaptic weight potential traces from different dendritic recording locations as (reference SI Appendix). The voltage criterion is fulfilled if the mapped onto the neuronal morphology during presentation of a local dendritic membrane potential exceeds a threshold of –40 mV preferred stimulus. SI Appendix,Fig.S5shows a similar plot, pro- viding more widespread dendritic recording locations together with for at least 26 ms (compare τNMDA = 26 ms). The current criterion combines an NMDA current threshold, equivalent to synaptic weight the activation of synapses on the dendrite from which the recording multiplied by 30% of the peak NMDA conductance at –40 mV, has been made. These simulations indicate that multiple distinct local dendritic Na+ spikes and NMDA spikes can be triggered near simultaneously on different dendrites across the morphology. Such representations provide us with a useful snapshot of mem- A brane potential at different locations in the neuron, yielding infor- mation which is not available from single-site electrophysiological recordings. However, it is still difficult to use such plots to assess the quantitative relationship between near-simultaneous events in different dendrites and their link to APs at the soma. We therefore

developed a representation of the overall spatiotemporal dynamics NEUROSCIENCE of membrane potential across the entire neuron by plotting a maximum membrane potential projection against time, with in- dividual dendritic Na+ spikes and NMDA spikes and their prop- agation identified using our detectors. These spatiotemporal panoramas allow us to track the evolution of individual events in space and time and determine their relationship with each other. B Fig. 3B shows an example of such a panorama, which represents the same events as shown in Fig. 3A, except across the entire morphology. An even more powerful representation of the spatiotemporal in- teractions between synaptic inputs, dendritic spikes, and APs is provided by animating such a spatiotemporal snapshot and an- notating it with active synapses (Movie S1). Such a movie allows the evolution of membrane potential to be linked to the location of synaptic inputs on the morphology. Next, we quantified where in the morphology dendritic Na+ spikes and NMDA spikes are initiated by plotting the fraction of spikes generated across the morphology during prolonged sim- Fig. 2. Detecting dendritic Na+ spikes and NMDA spikes. (A) Four examples ulations (Fig. 3C). This analysis indicates that most dendritic of local dendritic Na+ spikes showing dendritic membrane potential (Top), branches in the L2/3 pyramidal cell morphology support the + dendritic Na+ conductance (Center), and somatic membrane potential (Bot- generation of both dendritic Na spikes and NMDA spikes. The tom). We compared simulations in a fully active (light blue) and a passive frequency of initiation was approximately dependent on the dis- dendrite (gray) with identical synaptic input. Dendritic Na+ spikes (initiation tance from the soma, with the majority of dendritic events being indicated by dashed red lines) are characterized by a >10% voltage ampli- initiated in the most distal dendrites, and the most proximal tude difference (light red shading) between active and passive simulations. < μ + dendrites ( 50 m from the soma) representing unfavorable lo- We use a threshold (gray horizontal dashed line) on the local Na conduc- cations for initiation of dendritic spikes. These simulations also tance (Center, red) as a proxy to efficiently detect dendritic Na+ spikes in all indicate that it is unlikely that there exist discrete morphological following simulations. By simultaneously monitoring somatic Vm, we can “ ” distinguish local events from bAPs (gray vertical dashed lines; Materials and hotspots in the dendritic tree where dendritic spike initiation is Methods). (B) Three examples of local dendritic NMDA spikes showing particularly favorable, but rather that spike initiation probability is dendritic membrane potential (Top), local NMDA current (Center), and so- graded across the morphology. matic membrane potential (Bottom). We compared simulations in a dendrite with voltage-dependent NMDA conductances (light blue) and the same AP Output Strongly Depends on Dendritic Na+ Spikes and NMDA dendrite with NMDA conductances frozen at the resting potential (gray), Spikes. We linked dendritic spike initiation and AP output by with identical synaptic input. Dendritic NMDA spikes (initiation indicated by developing an approach for quantifying the spatial and temporal > dashed orange lines) are characterized by a 10% voltage amplitude dif- footprint of dendritic spikes that precede APs during a preferred ference (light orange shading) between active and passive simulations. We sensory stimulus. This involves detecting somatic APs and den- use a threshold (gray horizontal dashed line) on the local NMDA current (Center, orange) and a threshold on the local dendritic membrane potential, dritic spikes and then computing the spatiotemporal somatic AP- as well as a threshold on the total charge delivered during a spike, as a proxy triggered average of the dendritic spikes (Fig. 3D), taking into to efficiently detect dendritic NMDA spikes in all following simulations account the background (BG) frequency of dendritic spikes not (Materials and Methods). associated with an AP. The resulting plot shows that dendritic

Goetz et al. PNAS | 3of12 Active dendrites enable strong but sparse inputs to determine orientation selectivity https://doi.org/10.1073/pnas.2017339118 Downloaded by guest on October 1, 2021 A C D E μ m) spikes + spikes per AP + spikes per AP + Na

100 μm Distance from soma ( μ m) Additional Na Distance from soma ( 50 mV Fraction of initiated Na soma

Time (ms) Time before AP (ms) pre AP control B 10 0

m) –10 μ –20 –30 –40 –50 –60 Dendritic voltage (mV) Distance from soma ( μ m) NMDA spikes perNMDA AP Distance from soma (

–70 spikes perAdditional NMDA AP Fraction of initiated NMDA spikes Fraction of initiated NMDA –80

Time (ms) Time before AP (ms) AP pre control

Fig. 3. Dendritic Na+ spikes and NMDA spikes precede AP output. (A) Example recordings of local dendritic voltage at the location of dendritic Na+ spikes (red) and NMDA spikes (orange). Recording locations are shown on morphology (Left) with corresponding pipette colors. The intersection of voltage traces with the left vertical axis indicates distance from soma, while the scale bar shows the voltage scale. (B) Example snapshot of dendritic membrane potential as a function of space and time (same spatial and temporal extent as in A). Multiple dendritic Na+ spikes (initiation at red triangles; propagation indicated by white diamonds) and NMDA spikes (initiation at orange triangles) initiate and propagate across the dendritic tree. A bAP (blue triangle and white diamonds) occurs near time (t) = 54 ms. Contours are lines of equal membrane potential (maximum projection across all dendrites at this distance from the soma). (C) Distribution of the probability of initiating a dendritic Na+ spike (Top) or dendritic NMDA spike (Bottom) across the dendritic tree. (D) Spatiotemporal AP-triggered averages of dendritic Na+ spikes (Top) and NMDA spikes (Bottom), with BG dendritic spiking activity subtracted. Values in the red rectangles sum to the average numbers of dendritic events (shown in E) preceding a single AP. (E)NumberofdendriticNa+ spikes (mean ± SD; red, Top) and NMDA spikes (mean ± SD; orange, Bottom) preceding a single AP compared to random time points (control, gray).

Na+ spikes that are linked to output of the neuron (i.e., a so- Na+ spike, and 12.7 ± 0.8% of dendritic Na+ spikes occurred matic AP) can occur at all distances from the soma (aside from within 20 ms of a dendritic NMDA spike). the most proximal 50 μm, a region which is generally unfavorable for triggering local dendritic spikes; Fig. 3C). The largest number A Causal Link between Dendritic Spikes and Output APs. In the pre- of spikes occur in a zone ∼100 to 150 μm from the soma (which vious figure we showed that output APs are associated with an increase in dendritic spikes preceding these APs. To demonstrate includes some terminal branches). With respect to timing, the + + that these additional dendritic Na spikes and NMDA spikes majority of dendritic Na spikes occurred in the 5 ms prior to the causally drive somatic AP output, we selectively deleted the den- AP, with a long “foothill” of tens of milliseconds where dendritic dritic voltage-gated conductances (mediated by voltage-gated so- Na+ spikes could still influence axonal AP initiation (Fig. 3D, dium [Nav] channels and NMDA receptors) that are driving the Top). For NMDA spikes, the spatial distribution was comparable + + Na spikes and NMDA spikes, respectively. First, we removed to that of dendritic Na spikes, while the timing relationship was + dendritic Nav channels to prevent dendritic Na spikes and ex- broader with the peak shifted to more negative values (Fig. 3D, amined the consequences for AP output using identical synaptic Bottom). The latter effect is due to the much longer duration of input. Preventing dendritic Na+ spikes substantially reduced, on the NMDA spikes, which allows them to exert their effect on AP average from 6.0 to 2.3 Hz, but did not abolish output APs (Fig. 4 A initiation over a longer time window. In summary, the dendritic and B). Second, we blocked NMDA spikes by freezing the NMDA spikes associated with the triggering of an AP can originate and conductance at its resting potential value, thus removing NMDA- cooperate over almost the entire dendritic tree. based regenerative events while preserving an ohmic synaptic NMDA How many dendritic spikes are involved in triggering a single conductance. This completely abolished output APs (Fig. 4 A and B), AP? To provide an estimate, we counted the number of dendritic implying that NMDA spikes are more efficient than dendritic Na+ spikes occurring across the dendritic tree in a spatiotemporal spikes at driving AP output. Notably, AP output was abolished window corresponding to the peak temporal influence of the re- even while the mean at the soma was maintained spective spike types (Fig. 3D, red rectangles). This count revealed by constant somatic current injection. This suggests that NMDA that 9.9 ± 3.2 dendritic Na+ spikes occurred in the neuron in the spikes mainly drive APs not via their contribution to the average 15 ms prior to each AP (compared to 4.1 ± 2.6 spikes in a ran- membrane potential but rather by their contribution to large tran- sient somatic (39) that have been shown to precede domly selected control window of the same duration and spatial APs in vivo (40, 41). extent; Fig. 3E, Top). In contrast, 5.5 ± 2.3 NMDA spikes oc- + ± Removing dendritic Na spikes or NMDA spikes from pro- curred in the 40 ms prior to each AP (compared to 2.5 2.3 gressively larger numbers of dendritic branches (while again NMDA spikes in a randomly selected control window; Fig. 3E, maintaining the mean somatic membrane potential by constant Bottom). These results indicate that a surge in dendritic spike somatic current injection) revealed a nonlinear relationship be- activity across the dendritic tree leads to initiation of an AP, with a tween the number of manipulated branches and the output firing + 2.4- and 2.2-fold increase above baseline for dendritic Na spikes rate (Fig. 4C). In both cases, the relationship was described by an and NMDA spikes, respectively. Both types of dendritic spike exponential decay, which was steeper for NMDA spike removal tended to be triggered in concert with each other (69.0 ± 2.7% of than for dendritic Na+ spike removal (on average, freezing the dendritic NMDA spikes were triggered within 20 ms of a dendritic NMDA conductance in only 12 dendritic branches reduced the

4of12 | PNAS Goetz et al. https://doi.org/10.1073/pnas.2017339118 Active dendrites enable strong but sparse inputs to determine orientation selectivity Downloaded by guest on October 1, 2021 A B Fig. 4. Causal role of dendritic Na+ spikes and NMDA spikes in triggering AP output. (A) Example active dendrites recordings from the soma with a fully active den- dendritic Nav dritic tree (black), or when blocking dendritic Na+ blocked spikes (red), or NMDA spikes (orange) by blocking dendritic NMDAR dendritic Na channels, or freezing the voltage de- blocked v AP frequency (Hz) AP pendence of the NMDA conductance at the resting Somatic voltage (mV)

control Nav NMDAR potential, respectively, while maintaining the mean Time (ms) block block somatic membrane potential by somatic current in- C jection. (B) Blocking dendritic Na+ spikes (red) and NMDA spikes (orange) in the entire dendritic tree reduces AP output relative to a fully active dendritic tree (black). Mean somatic membrane potential was maintained as in A.(C) Blocking dendritic Na+ spikes

frequency (Hz) (red, Left) and NMDA spikes (orange, Right)inan P AP frequency (Hz) AP A increasing number of randomly chosen individual dendrites leads to a decrease in AP output frequency that can be fit with an exponential decay. Mean so- Number of dendrites without Na+ spikes Number of dendrites without NMDA spikes matic membrane potential was kept constant as in A.

somatic output rate to 1/e of the control value, while deletion of dendritic morphology, dendritic location of the synapse, and in Nav channels in 32 dendritic branches was necessary to achieve particular the number of cooperating synapses are also impor- the same effect at the soma). The stronger impact of NMDA tant. Notably, synapses which trigger dendritic spikes in coop- conductance freezing compared with Nav removal is consistent eration with other synapses can include both strong and weak with our simulations using spatially widespread manipulations synapses (Fig. 5E, red and orange). However, synapses which can (Fig. 4 A and B), as well as with experimental results on the single-handedly trigger local dendritic spikes originate exclu- impact of dendritic NMDARs on neuronal output (13, 17). sively from the large-conductance tail of the lognormal synaptic weight distribution (Fig. 5E, magenta and yellow). In these cases,

Which Synaptic Inputs Are Most Important for Triggering Dendritic the dendritic spike was initiated at the location of this synapse NEUROSCIENCE Spikes? We next turned to the question which constellations of (Fig. 5G). What is the functional impact of this subset of strong active synapses are most successful in triggering dendritic synapses, which we show have disproportional power in trigger- spikes. To determine the spatial and temporal scale over which ing dendritic spikes? synapses interact to trigger a dendritic spike, we first mapped the locations and timing of excitatory synaptic inputs relative to the Dendritic Spikes Enable the Strongest 1% of Synapses to Determine initiation of a dendritic Na+ spike or NMDA spike (Fig. 5A). Orientation Tuning of AP Output. Since the generation of APs in- This was quantified and visualized using spatiotemporal den- volves a threshold, they are often more sharply tuned than the dritic spike–triggered averages (STA) for dendritic Na+ spikes average of the synaptic inputs triggering them, a phenomenon (Fig. 5B, Left) and NMDA spikes (Fig. 5B, Right). In the case of known as the “iceberg effect” (42, 43). This effect has previously dendritic Na+ spikes, most active synapses were located within been observed for orientation selectivity in L2/3 neurons in V1 ∼20 μm of the initiation site, and their activation preceded the (33, 36) and is reproduced by the model (SI Appendix, Fig. S6). initiation of the spike by less than 2 ms (Fig. 5B, Left). Most Can dendritic spikes contribute to sharpening of AP tuning by NMDA spikes were triggered by synapses located at the initia- nonlinearly amplifying and selectively weighting different synaptic tion site and were activated less than 1 ms before spike initiation inputs? To investigate this, we measured the orientation tuning of (Fig. 5B, Right). dendritic Na+ spikes, NMDA spikes, subthreshold membrane To determine how many active excitatory synapses are required potential at the soma, and the AP output. As shown in Fig. 6 A to trigger a dendritic spike, we counted the number of active and B, orientation selectivity index (OSI) values—with the ex- synapses in a spatiotemporal window containing the peak tem- ception of somatic VmOSI, which is low both in the experiment poral incidence of synaptic activation preceding dendritic spike (17) and in our model as it reflects the subthreshold tuning before initiation (Fig. 5B, red rectangles: up to 100 μm from the initiation application of the somatic iceberg effect—increase progressively site and 4 or 1.5 ms before the initiation of a Na+ spike or NMDA from synaptic input via dendritic Na+ spikes and NMDA spikes to spike, respectively). On average, a single dendritic Na+ spike was AP output (see also SI Appendix,Fig.S7for full OSI distributions). triggered by 2.3 ± 1.4 active excitatory synapses, and a single This progression indicates that active dendrites enable two iceberg NMDA spike was triggered by 1.6 ± 0.9 active excitatory synapses effects to enhance tuned responses to in vivo synaptic inputs: the (Fig. 5C). In some cases, even a single synapse is sufficient to first is the conversion of synaptic input to dendritic spikes, and the trigger either a dendritic Na+ spike or an NMDA spike (Fig. 5D). second involves their transformation into output APs. To test this model, we directly measured the impact of dendritic Strong but Sparse Synaptic Inputs Trigger Dendritic Spikes. Are all spikes on the orientation tuning of AP output. We abolished ei- synapses equal in their ability to trigger dendritic spikes, or are ther dendritic Na+ spikes by blocking dendritic Na+ conductances there “privileged” synapses with respect to dendritic spike initi- (Fig. 6 A and B, Center Left and SI Appendix,Fig.S7B)orNMDA ation? We plotted the probability that activation of a synapse spikes by freezing the voltage dependence of the NMDA con- leads to successful initiation of a dendritic spike as a function of ductance (Fig. 6 A and B, Center Right and SI Appendix,Fig.S7C) peak synaptic conductance (Fig. 5F). This revealed a sigmoidal while maintaining the mean AP frequency by somatic current in- relationship: the probability of success is low for synapses with jection. When NMDA spikes were blocked, both the somatic less than 0.5 nS peak conductance, increases severalfold from 0.5 subthreshold membrane potential tuning (as measured by the to 2 nS peak conductance, and saturates for larger conductances. membrane potential OSI, VmOSI) and the tuning of AP output Thus, synaptic conductance is the major determinant of the were weakened compared to control conditions (Fig. 6 A and B, efficacy of a synapse in evoking dendritic spikes. However, the Left and Center Right and SI Appendix,Fig.S7C). Blocking dendritic + scatter in the relationship indicates that other factors, such as Na spikes did not strongly affect VmOSI nor AP output OSI

Goetz et al. PNAS | 5of12 Active dendrites enable strong but sparse inputs to determine orientation selectivity https://doi.org/10.1073/pnas.2017339118 Downloaded by guest on October 1, 2021 Fig. 5. Surprisingly few synaptic inputs are re- AB spike quired to trigger dendritic spikes. (A) Schematic of the μ m) spike spatiotemporal dendritic STA used in B. Circles of in- + creasing diameter and increasingly “hot” colors indi- cate synaptic inputs with increasing synaptic strength (scale in G). (B) STA for dendritic Na+ spikes (Left) and dendritic NMDA spikes (Right), with the BG level of Distance from initiation site Distance from recording synaptic activity subtracted. Colormaps are clipped. TimeTime beforebefore spike spike Distance from initiation site ( Additional synapses per Na

Red rectangles indicate spatiotemporal windows for Additional synapses per NMDA counting synaptic inputs in C.(C) Number of excit- Time before Na+ spike (ms) Time before NMDA spike (ms) atory synaptic inputs active before dendritic Na+ CD E + spikes (mean ± SD; red, Top) and NMDA spikes spike (mean ± SD; orange, Bottom), compared to the + spikes number of active synapses in control spatiotemporal + windows placed at random time points (gray; Mate- + rials and Methods). (D) Dendritic Na spikes (red, % of Na Synapses per Na

Top) and NMDA spikes (orange, Bottom) broken Fraction of synapses down by the number of synapses that triggered them. + Synapses pre-Na+ spike Synaptic strength (nS) pre Na random Gray bars show the distribution of the number of ac- spike tive inputs in control spatiotemporal windows. (E) Distribution of the strength of synapses activated preceding a random control timepoint (gray), den- dritic Na+ spikes (Top, red colors), and NMDA spikes (Bottom, orange colors). For dendritic Na+ spikes and NMDA spikes, this distribution can be further split into cooperative trigger synapses (red and orange) and % of NMDA spikes % of NMDA Synapses per NMDA spike Synapses per NMDA individual trigger synapses (magenta and yellow). The Fraction of synapses dots represent the mean values of the respective dis- Synapses pre-NMDA spike Synaptic strength (nS) tribution. Note the peak at 0.1 nS resulting from BG random synapses (w = 0.1 nS) that contribute to dendritic Na+ pre NMDAspike Control One synapse removed spikes and NMDA spikes. “Cooperative synapses” are F G synapses where more than one synapse was active in the spatiotemporal window preceding the dendritic ≥ 3.0 5.2 spike, whereas if only a single synapse was active 0.2 5.1 during this window, we call this an “individual trigger 0.1 synapse.” (F) Average probability for a synapse to 5.0≤ Strength (nS)

+ Dendritic voltage (mV)

trigger a local dendritic Na spike (red) or NMDA spike Distance from soma ( μ m) (orange) as a function of synaptic strength. (G, Left) P(success|synaptic strength) 26 27 9282 30 13 26 27 9282 30 13 Synaptic strength (nS) Time (ms) Time (ms) Snapshot of synaptic inputs across the dendritic tree NMDA spike initiation (circles; brighter color indicates larger synaptic weight) Na+ spike initiation Na+ spike propagation contributing to the initiation of a dendritic Na+ spike. (Right) Silencing a strong trigger synapse (yellow circle at t = 27.6 ms, marked with a star on the Left) abolishes the dendritic Na+ spike. Contours are lines of equal membrane potential (maximum projection across all dendrites at this distance from soma, as in Fig. 3B).

(Fig. 6 A and B, Center Left and SI Appendix,Fig.S7B). However, its value at the resting potential, twice the number (82 synapses) simultaneous block of dendritic Na+ spikes and NMDA spikes needed to be deleted to achieve the same reduction in AP output strongly reduced both VmOSI and output OSI (Fig. 6 A and B, Right (Fig. 6C, Top). When dendritic Nav was blocked in addition to and SI Appendix,Fig.S7D), indicating that dendritic spikes con- freezing the NMDA conductance, the number of synapses to be tribute substantially to the orientation tuning of AP output. Fig. 6B deleted increased further to on average 95. Interestingly, the also shows that the tuning of dendritic Na+ spikes and NMDA relationship was much more linear when random synaptic inputs spikes is reduced when the other type of dendritic spike is blocked, as opposed to the strongest ones were removed (Fig. 6C, Bot- respectively, suggesting that they act cooperatively. A hallmark of tom). Thus, compared to passive dendritic integration, dendritic this cooperativity, the combined contribution of dendritic Na+ spikes further amplify the efficacy of strong synapses in triggering spikes and NMDA spikes to AP output, exceeds the linear sum of APs at the soma. their individual contributions (Fig. 4B): the firing rates when either dendritic spike is blocked (2.3 and 0 Hz) sum to less than the rate Discussion when they are both present (6.0 Hz). We have developed a realistic model of dendritic integration These results suggest that sharply tuned, strong synaptic inputs, during sensory processing in vivo to address a longstanding selectively amplified by dendritic spikes, have a disproportionate question in neuroscience: how do active dendrites contribute to effect on the tuning of somatic output. To test this idea, we “de- determining the stimulus selectivity of a neuron? Despite decades leted” inputs from the preferred input pool and measured the of work (44, 45), we still lack a good understanding of how neu- effect on AP output (Fig. 6C, Top). In all conditions, the rela- rons in primary sensory cortex respond selectively to a particular tionship was described by an exponential decay, which was less stimulus feature given a barrage of weakly selective inputs. Our steep when the NMDAR conductance was frozen alone or in model provides a mechanistic explanation for how narrowly tuned combination with a block of Nav, making the dendritic tree pas- orientation-selective responses can arise from dendritic integra- sive. We found that on average, removing as few as 46 of the tion of weakly tuned synaptic input: a few strong synapses, which strongest synapses, corresponding to less than 1% of the total provide input from similarly tuned presynaptic neurons, prefer- synaptic input population, reduced AP output to 1/e of the initial entially trigger dendritic spikes. Dendritic spikes in turn are more value in the active model. Importantly, this effect relied on den- narrowly tuned to orientation than the synaptic input and efficiently dritic NMDA spikes: when the NMDA conductance was frozen to drive the majority of somatic AP output. Thus, by triggering

6of12 | PNAS Goetz et al. https://doi.org/10.1073/pnas.2017339118 Active dendrites enable strong but sparse inputs to determine orientation selectivity Downloaded by guest on October 1, 2021 A Fig. 6. Dendritic spikes enhance control of AP out- Control Dendritic Nav frozen NMDAR frozen NMDAR & Nav frozen put and its tuning by a small number of strong syn- aptic inputs. (A) Example of the tuning of dendritic Na+ spikes (red) and NMDA spikes (orange) as well as Na+ spike NMDA spike tuning tuning subthreshold somatic membrane potential (gray) and APs (black), under control conditions and with dendritic Na+ spikes (second from Left), NMDA spikes (third from Left), or both (Right) blocked. (B) Mean AP tuning and + Vm subthreshold tuning OSI of dendritic Na spikes (red), NMDA spikes (or-

ange), somatic Vm (gray), and APs (black) under control conditions (Left), with Nav channels blocked (second from Left), with NMDA conductances frozen (third from Left), or both (Right). (C, Top) Removing strong synapses decreases AP frequency in response B to a preferred visual stimulus in the full model (black)

and under Nav channel block (red). The decrease can be fit with an exponential decay and is less steep

OSI when NMDARs only (orange) or NMDARs and Nav channels (purple) are blocked. Constant current was injected at the soma to maintain AP frequency at control levels with zero synapses removed. This was + + + + done to engage the somatic output nonlinearity at Vm Vm Vm Vm Na Na Na Na APs APs APs APs the same starting point as in control. (Bottom) Re- NMDA NMDA NMDA NMDA moving random synapses decreases AP frequency in C dendritic Nav blocked D response to a preferred visual stimulus in the full dendritic NMDAR blocked model (black) and under Nav channel block (red). The both blocked decrease can be fit with an exponential decay. When control NMDARs only (orange) or NMDARs and Nav channels (purple) are blocked, the decrease can be fit linearly

AP frequency (Hz) AP and is less steep. (D, Top) Schematic of the compo- sition of spatiotemporal STAs of synaptic activity (see NEUROSCIENCE Number of removed synapses (strongest) Fig. 5 A and B) and a spatiotemporal AP-triggered 00 0.50.5 1 average of dendritic spikes (see Fig. 3 A and D). We OSIOSI used these tools to dissect the spatiotemporal con- stellations of synaptic inputs that evoke dendritic spikes and the effect of such dendritic spikes on AP

spikes output. (Bottom) OSI increases from synaptic input via dendritic spikes to AP output. We show the OSI of synaptic inputs (light blue: all synapses; dark blue: AP frequency (Hz) AP + 0.90 0.92 strong synapses), dendritic Na spikes (red), and

Number of removed synapses (random) Orientation Selectivity Index NMDA spikes (orange) as well as subthreshold so- matic membrane potential (gray) and APs (black).

dendritic spikes, a small subset of strong synapses drives amplifi- (18, 31), with strong synapses preferentially tuned to a similar cation of orientation-selective signals, effectively determining the orientation as the postsynaptic neuron (18). tuning of neuronal output. They do so in the context of the activity Because no direct and complete recordings of the synaptic of other excitatory and inhibitory synapses on nearby dendrites, input received by an L2/3 neuron in mouse V1 are available, we which can modulate their gain and thus implement a rich spectrum used patch-clamp recordings from the dendrites of L2/3 pyramidal of nonlinear computations in dendrites (4, 46–48). These results neurons in mouse V1 in vivo (17) to constrain dendritic excitability indicate that active dendrites play an essential role in shaping and membrane potential dynamics during sensory processing. stimulus selectivity in cortical circuits and have important implica- These dendritic recordings (see also ref. 12) present especially tions for coding and connectivity in sensory cortex. valuable sets of constraints because they allow dendritic events to be recorded directly with high resolution and because the spatial An Active Dendritic Model of In Vivo Synaptic Integration. To study and temporal structure of synaptic input during sensory processing the mechanisms of synaptic integration during visual stimulation is still actively debated. In particular, evidence for spatial clus- tering of active synapses varies between different cell types, in vivo, we have built and combined models of synaptic input and – the postsynaptic pyramidal neuron that are constrained by a regions, and species (32 37, 53, 54). We therefore followed an approach in which synaptic inputs are placed randomly across the large set of experimental data obtained in vitro (18, 22, 23, 49) dendritic tree and activated independently of each other, with any and in vivo (17, 18, 20, 21, 23, 24). As with all biophysical models spatial or temporal clustering occurring by chance. Our simula- of neurons, biological variability in parameters including morphol- tions show that this is sufficient to reproduce the pattern of den- ogy, conductance densities, and synaptic weights leads to different dritic Na+ spikes and NMDA spikes observed in vivo. We also parameter combinations that generate similar neural responses (50, show that implementing spatial clustering of cotuned excitatory 51) by relying on compensatory effects. The properties of real inputs (32, 35, 36) has only a small effect on the orientation se- neurons will therefore differ from each other and from our model, lectivity of dendritic spikes in our model (SI Appendix,Fig.S8), allowing alternative scenarios for dendritic integration. The com- with the exception of the orientation selectivity of dendritic Na+ bined model reproduced characteristic dendritic spike waveforms spikes, which increased with clustering when dendritic NMDA and event statistics by using the sparse in vivo synaptic input pat- spikes were blocked. Thus, spatial clustering of cotuned synaptic terns that are implied by recent experiments (20, 52). A key as- input does not fundamentally change our conclusions about the sumption was to use a lognormal distribution of synaptic weights, relationship between synaptic input, dendritic spikes, and AP based on recordings from synaptically connected pairs of neurons output.

Goetz et al. PNAS | 7of12 Active dendrites enable strong but sparse inputs to determine orientation selectivity https://doi.org/10.1073/pnas.2017339118 Downloaded by guest on October 1, 2021 Few Synaptic Inputs Are Sufficient to Drive Dendritic Spikes In Vivo. transients so they reach threshold for triggering APs, without The relationship between synaptic input in vivo and dendritic strongly affecting the mean membrane potential at the soma. spikes in vivo is unknown. Here, we show that a small number of synaptic inputs can be sufficient to trigger a dendritic spike under Output Tuning Is Determined by Dendritic Spikes. The prevailing in vivo conditions. In contrast, previous experimental work on view of synaptic integration is that the preferred orientation, and pyramidal cells in brain slices suggested that many synaptic in- the tuning width of the output of a neuron, are set by the sum of puts are required to engage dendritic nonlinearities (39, 55, 56). its synaptic inputs and the nonlinearity of AP generation (33, 37, Even with synchronous activation of inputs, activation of several 71–73). Even in models where the distribution of synaptic weights tens of synapses was required to trigger dendritic spikes (57, 58). is taken into account (18, 74), a predominantly linear sum of those While early theoretical work suggested that single synapses could inputs drives somatic membrane potential fluctuations (75), and trigger regenerative events confined to a single spine head, these the sharpness of output tuning is effectively set by the somatic AP studies used very high spine neck resistances (59–61). More re- threshold. However, this single “iceberg effect” (42, 43) at the cent theoretical work has suggested that larger numbers of syn- soma cannot explain the almost complete suppression of AP chronized synaptic inputs are needed to initiate regenerative output by intracellular MK-801 block of NMDAR-mediated syn- NMDA events in dendrites (39, 62) and to reproduce experi- aptic nonlinearities observed in vivo (11, 13, 17). Furthermore, mentally observed AP firing patterns in cortical pyramidal neu- direct dendritic recordings from neurons in mouse V1 show a rons (63, 64). progressive increase in orientation selectivity from synaptic input Our work complements these findings and suggests that during via dendritic spikes to AP output, while subthreshold somatic sensory processing, surprisingly few, but strong synaptic inputs— membrane potential remains weakly tuned (17). Here, we dem- acting on top of BG depolarization provided by randomly acti- onstrate a mechanism that provides an explanation for these re- vated synapses elsewhere in the dendritic tree (SI Appendix, Fig. sults: well-tuned, strong synapses are privileged in their ability to S9)—can be sufficient to trigger local dendritic Na+ spikes and trigger dendritic spikes, which in turn drive AP output. This NMDA spikes. The discrepancy with previous experimental and mechanism effectively corresponds to two iceberg effects in series theoretical work can be explained by the properties of the synaptic (Fig. 6D): the first being dendritic (and thus implemented locally input that is present in vivo but absent in slices. Earlier attempts to and in parallel in different dendritic branches), resulting from the include in vivo–like synaptic input to dendrites (39, 65–69) did not selective amplification of synaptic inputs by dendritic spikes, and use realistic input weight distributions, which we have constrained the second being axosomatic, a global threshold for neuronal using recent experimental data (18), featuring a tail of strong output. It is likely that the nonlinearities underlying these two synapses among many weaker ones, a key element of our synaptic iceberg effects can implement more general dendritic computa- input model. Moreover, the advent of direct dendritic recordings tions beyond orientation tuning (76). To demonstrate this mech- of membrane potential in vivo during sensory processing (17) has anism directly, we performed simulations in which we blocked now allowed us to provide more rigorous constraints on the fre- dendritic Na+ spikes or NMDA spikes while matching the mean quencies and properties of active dendritic events in vivo. How- somatic firing rate by constant somatic current injection. In this ever, our results do not rule out alternative scenarios in which case, output tuning selectivity is degraded (Fig. 6 A and B). In larger numbers of coactive, weaker synapses cooperate to generate summary, dendritic spikes are an essential step in the trans- dendritic spikes. formation of synaptic input tuning to neuronal output tuning. Im- portantly, we show that active dendrites strongly reduce the number Dendritic Spikes Strongly Influence AP Output In Vivo. How many of synapses that are required to determine output tuning, compared dendritic Na+ spikes and NMDA spikes are required to trigger a to a model without dendrites (18). single somatic AP? We used spatiotemporal AP-triggered aver- aging to identify dendritic events leading up to a somatic AP. On Implications for Circuit Function. We demonstrate that a small average, 5.5 ± 2.3 NMDA spikes and 9.9 ± 3.2 dendritic Na+ fraction of strong synaptic inputs can determine postsynaptic spikes occurred in the relevant time windows before a single AP. output and its tuning. What are the implications of such a sparse Recent in vivo two-photon imaging studies have suggested that input representation for the function of single neurons and for local dendritic events are almost always part of a synchronized, the operation of the circuit? First, sparser synaptic connectivity multibranch depolarization of the dendrites that is associated allows more robust storage of a given number of patterns in with somatic AP firing (54, 70). Our results indicate that dendritic recurrent neural networks (77). Second, heavy-tailed synaptic events often drive somatic APs, which explains these findings; weight distributions allow neural circuits to respond faster, have however, we also find isolated dendritic events that would be more a larger dynamical range, and be less sensitive to random fluc- difficult to detect using calcium imaging methods. Our modeling tuations in synaptic activity (74), compared to networks with nor- approach also allows us to show that dendritic Na+ spikes and mally distributed synaptic weights. Finally, computational and NMDA spikes provide different contributions to AP generation empirical evidence suggests that sparse, strong synapses embed- and AP tuning: NMDA spikes are good amplifiers even of single ded within a large pool of weak synaptic inputs might allow the inputs, and a small number of spikes can drive somatic AP output neuron to “reside one synaptic input away from the threshold” (Fig. 3), which inherits their tuning (Fig. 6). Conversely, each (78). The resulting strong correlations in activity between pre- and dendritic Na+ spike represents integration over a larger number of postsynaptic neurons connected by strong synapses have indeed synaptic inputs, forming an average of their sensory tuning—and been observed in vivo (18) and may be both cause and conse- in turn more dendritic Na+ spikes are required to drive a single quence of the creating and maintaining the somatic AP. functional architecture of the circuit. Our simulations also explain an apparently paradoxical ex- By amplifying the effect of strong synaptic inputs and helping perimental finding: using intracellular MK-801 to block NMDA them to reach threshold for the somatic AP, active dendrites receptors almost completely prevents AP output, while mean so- enable an even sparser input representation than passive den- matic membrane potential is little affected (11, 13, 17). Our model drites (Fig. 6C). Active dendrites therefore provide several ad- reproduces these results (Fig. 4 A and B), and using a cumulative vantages. First, encoding stimulus features with a smaller number block of NMDA spikes in individual dendrites, (Fig. 4C)wepro- of active neurons further increases the energy efficiency of the vide a causal link between NMDA spike generation and AP output circuit (79), as chemical synaptic transmission is energetically at the soma. Specifically, NMDA spikes in individual dendritic costly (80) and AP propagation in presynaptic is more ex- branches provide substantial amplification of membrane potential pensive than having active dendrites (81). Second, the large

8of12 | PNAS Goetz et al. https://doi.org/10.1073/pnas.2017339118 Active dendrites enable strong but sparse inputs to determine orientation selectivity Downloaded by guest on October 1, 2021 number of “background” synapses with small weights could pro- with or without block of NMDA spikes by postsynaptic MK-801 vide the neuron with a reservoir to represent new stimuli through (11, 13, 17). The effect on AP output could then be compared to synaptic plasticity. For example, a recent model of (82) the predictions of our model (Fig. 6C). suggests that in the absence of dendritic amplification, weak syn- Finally, the quantitative relationships we predict between syn- aptic input only minimally affects AP output, while plateau po- aptic input, dendritic spikes, and somatic output may eventually be tentials not only drive somatic output but also lead to synaptic directly experimentally testable. This would require simulta- weight updates (83). Finally, nonlinear subunits in active dendrites neously measuring synaptic input patterns and dendritic voltage increase the number of input patterns that can be stored and across the entire dendritic tree in vivo, while monitoring somatic nonlinearly discriminated (76). output. This is an unprecedented experiment, which represents a Given that a small number of strong inputs can determine major technical challenge, but recent developments in rapid three- output tuning, this leaves open the question of the immediate dimensional two-photon imaging techniques (95–99), in combi- functional role of the majority of weaker synaptic inputs. First, nation with the use of new generations of genetically encoded they can provide weakly or untuned BG depolarization (18) to sensors of glutamate (100) and voltage (101), may allow the de- — allow dendritic spikes which are driven by the sparse, highly cisive measurements to be made. tuned input—to trigger output APs. Second, they might be in- volved in a distributed representation of more complex visual Conclusions stimuli, such as natural scenes (53). In this way, they could allow By synthesizing the latest data on synaptic connectivity, synaptic dendritic mechanisms to implement computations that had weight distributions, and dendritic excitability in V1 in vivo, we previously been ascribed to network function, such as complex have shown that the selective amplification of the strongest 1% cell responses (7) and binocular disparity (3). Third, they could of synaptic inputs by dendritic spikes enables them to determine carry additional information about brain state and modulate somatic AP output and its tuning. This occurs in a two-step postsynaptic response properties depending on the level of at- process, whereby a small number of strong synapses trigger local tention or motion of the animal (20, 84, 85). Finally, coactivation dendritic NMDA spikes and Na+ spikes, and few dendritic spikes of local groups of weaker synapses could emulate the activation in turn are sufficient to drive AP output. As a consequence, many of a strong synapse (37), also in the recruitment of dendritic synapses are freed up to encode other input features, increasing spikes (39, 86, 87). We expect the mechanism described here to generalize to the computational capacity of the postsynaptic neuron and the neurons in any neural circuit where sparse synaptic inputs engage surrounding circuit. Ultimately, this design provides the local postsynaptic dendritic nonlinearities. It should be particularly network with great flexibility for learning: only a small number of NEUROSCIENCE relevant in sensory systems where different sensory features are connections need to be changed to encode a different stimulus represented by a subnetwork of strongly coupled neurons with and alter the response properties of a neuron. similar response properties, such as in barrel cortex (88, 89). Materials and Methods While our quantitative predictions are based on responses in well-tuned L2/3 pyramidal neurons in mouse V1, the NMDA L2/3 Pyramidal Cell Compartmental Model. All simulations were performed using NEURON [version 7.4 (102)] and Python (version 2.7/IPython version spikes and dendritic Na+ spikes studied here illustrate a more 5.1). We used a detailed morphology of a L2/3 pyramidal neuron filled with general principle of single neuron computation: dendritic excit- horseradish peroxidase (neuromorpho.org, archive Martin, NMO_00904), as ability serves to selectively amplify the impact of a subset of used in Smith et al. (17). To improve the fit between model and in vivo + strong synaptic inputs. In cells that do not support dendritic Na experiments, we added an axon initial segment and axon hillock (reference

spikes or NMDA plateau potentials, NMDA current boosting SI Appendix, Table S1 for parameters). Passive parameters were Cm = 1.0 2 2 (90) might provide sufficient input amplification to cross threshold μF/cm ,Rm = 15,000 Ω cm , and Ra = 150 Ω cm. We used voltage-activated for AP generation. This amplification could also be performed by Na+ channels (103), fast and slow voltage-activated K+ channels (104), other nonlinear dendritic mechanisms, such as dendritic Ca2+ M-type K+ channels, high- and low-voltage–activated Ca2+ channels, and spikes (91) or BAC firing (92). Ca2+-activated K+ channels (reference SI Appendix, Table S1 for parameters and channel model references). Conductance densities in the axon, axon Experimentally Testable Predictions. Our results lead to several initial segment and hillock, soma, and dendrites are given in SI Appendix, = − = = – experimentally testable predictions. First, our model predicts that Table S1. Reversal potentials were Eleak 80 mV, ENa 60 mV, EK 80 mV, = activating a small number of strong synaptic inputs in addition to a and ECa 140 mV. The voltage dependence of activation and inactivation of sensory stimulus 45° off from the preferred orientation should all voltage-gated ion channels was shifted by 18.5 mV in the soma and by 13.5 mV in the axon and dendrites, and kinetics were scaled for a nominal increase AP output to match the original sensory response to the temperature of 37 °C. The passive and active model properties satisfy a large preferred orientation. This number should be insufficient if ran- range of constraints from experiments in vitro and in vivo (SI Appendix,Fig.S1). domly chosen synaptic inputs of average weight are activated, or if dendritic spikes are inactivated, for example, using targeted In Vivo Synaptic Input Model. We used numerous experimental findings to pharmacological intervention (13). The necessary experiment constrain our synaptic input model. Briefly, we calculated the average single would require mapping the orientation selectivity of presynaptic synaptic conductance based on experimentally measured somatic excitatory neurons and a postsynaptic neuron and targeted postsynaptic potential (EPSP) amplitudes (18), taking into account dendritic (93, 94) of a set of presynaptic neurons whose tuning is similar to morphology (our simulations) and the number of synapses per contact (19, that of the postsynaptic neuron. 105). The conductances of individual excitatory signal synapses were then Second, we predict that the response to a preferred grating drawn from a lognormal distribution (28, 31) with this mean value, and each orientation should decrease to a level corresponding to 45° off synapse was assigned a mean presynaptic firing rate for each sensory stim- the preferred orientation when a small number of strong syn- ulus condition. The time-averaged total synaptic conductance was kept apses coding for the preferred orientation are successively “re- consistent with measurements obtained from in vivo whole-cell voltage- moved,” or inactivated. Importantly, this effect should be absent if clamp recordings (20, 52). Under a realistic overall firing rate distribution (17, 18) this yielded a total number of synaptic inputs consistent with ana- the same number of random synapses are inactivated or if den- tomical data. Regarding the spatial and temporal distribution of synaptic dritic spikes are pharmacologically inactivated. To test this pre- inputs on the dendritic tree, we make the simplest possible (and conserva- diction, one could characterize the sensory response properties of tive) assumption that synaptic inputs are independent of each other, and are presynaptic neurons, then progressively inactivate those presyn- randomly distributed in space across the postsynaptic dendrites, as well as aptic neurons whose response properties are most similar to those randomly activated in time (Discussion). The random placement of synapses of the postsynaptic neuron using targeted optogenetics (93, 94), in the dendritic tree is consistent with the recent results of Park et al. (106),

Goetz et al. PNAS | 9of12 Active dendrites enable strong but sparse inputs to determine orientation selectivity https://doi.org/10.1073/pnas.2017339118 Downloaded by guest on October 1, 2021 who used ablation of L2/3 pyramidal neuron dendrites to show that there is distribution of somatic EPSP amplitudes. BG excitatory synapses had a fixed no “master dendrite” which controls orientation selectivity. conductance of 0.1 nS. Furthermore, we used an NMDA:AMPA ratio = 1 (17) Number and spatial distribution of synapses. The model L2/3 neuron receives for all excitatory synapses and verified that this produced results consistent 5,001 synaptic contacts, of which 25% are inhibitory (25). Furthermore, 50% with experimental data (ref. 111, Fig. 6 A and B) (ref. 112, Fig. 3). The GABA of inhibitory synapses were located perisomatically (107). To achieve a ran- peak conductance was 0.1 nS, GABA reversal potential was –80 mV, and ki-

dom spatial distribution of excitatory synapses on the dendritic tree (49), we netics as in ref. 17, with the exception of τriseAMPA = 0.5 ms and τdecayNMDA = proceeded as follows: for any given synapse, a dendrite was randomly 26 ms (111). chosen with a probability matching its fractional surface area, and a location Implementation of synaptic input for different visual stimulus orientations. Neurons on the dendrite was chosen from a uniform distribution of relative positions with similar receptive field (RF) properties are more likely to be connected along its length (ranging from 0 to 1). For inhibitory synapses, 50% were and share stronger synaptic connections than neurons with unrelated RF randomly distributed across the dendritic tree according to the same rules as properties (18, 113). To emulate both findings in the synaptic input model, excitatory synapses. Of the remaining inhibitory synapses, 80% were placed we first distributed the 3,000 excitatory signal synapses into 16 bins directly on the soma and 20% were randomly distributed on the four den- according to an empirical function of their spatial RF correlation with the drites branching off the soma. postsynaptic neuron (SI Appendix, Fig. S2B, blue bars) following the distri- Functional clustering of synapses. To reproduce experimental results from bution of pairwise RF correlations observed in the experiment (ref. 18 Wilson et al. (36), we simulated functionally clustered synaptic inputs in a Fig. 2G, blue histogram). We then implemented the dependence of somatic subset of simulations. To match the dispersion of orientation preferences of EPSP amplitude on spatial RF correlation observed in the experiment by synaptic inputs along the dendrite measured by Wilson and colleagues (36), repeatedly swapping synaptic conductance values between pairs of spatial we fitted a Gaussian to the spiking response of each synapse, to four dif- RF correlation bins and accepting a swap if the mean synaptic weight in each ferent orientations, 0°, 45°, 90°, and 135°, and calculated its preferred ori- spatial RF correlation bin improved the approximation of the exponential entation. We then calculated the difference in orientation preference across relationship (ref. 18, refer to Extended Data Fig. 5D). The number of swaps all synapses. To generate clusters of similarly tuned synapses, we split the was chosen to approximate the scatter in ref. 18 (refer to Fig. 2G, circles). dendritic tree into regions of interest (ROIs) of ∼20-μm length (mean ± SD = This procedure results in stronger conductances being preferentially, but 19.9 ± 3.6 μm) within which experimental work has identified clustering or not exclusively, assigned to synapses with larger spatial RF correlations apparently random synaptic organization (33, 36, 37, 53, 54). We then cal- with the postsynaptic neuron (SI Appendix,Fig.S2B, Bottom)whilethe culated the circular dispersion (36) of the orientation preferences of syn- overall distribution of synaptic conductances remains lognormal (SI Appendix, apses in each ROI. Next, we swapped the location of the synapse with the Fig. S2B, Top). highest contribution to the circular dispersion with another randomly cho- Spatial RFs computed by reverse correlation with natural images using the sen synapse; we then recalculated the circular dispersion for all synapses in pseudoinverse method employed by Cossell et al. (18) have been shown to the two ROIs affected by the new locations generated by the swap: if the predict the optimum orientation of the same cells in response to drifting new locations reduced the mean circular dispersion, we accepted them, but gratings with high accuracy (114). However, spatial RF correlation can be if the new locations increased or did not change the mean circular disper- small and even negative for two neurons with similar orientation preference sion, we rejected the swap. We repeated this swapping procedure until the (18). Thus, the procedure of assigning conductance values to synapses bin- mean circular dispersion of all synapses was equal to or less than 15°. Our ned according to spatial RF correlation (SI Appendix, Fig. S2B, Bottom)in- final “clustered” model had a circular dispersion of 15.0° ± 6.7° (mean ± SD), troduces additional variability in synaptic conductance to inputs that may in in agreement with experimental data (36). fact have similar orientation preference. In vivo–like synaptic activation. Two thirds of synapses (“signal synapses”) were Finally, the orientation of the visual stimulus was defined by different driven by an inhomogeneous Poisson process (108), with a mean firing rate empirical distributions of firing rates of the presynaptic inputs (SI Appendix, of 1.37 ± 0.23 Hz (excitatory) or 6.0 Hz (inhibitory), consistent with refs 17 Fig. S2C, cityscape histograms). During presentation of a stimulus at the and 20. Notably, a characteristic feature of synaptic input during visual preferred orientation of the postsynaptic neuron, 90°, synapses with a sim- stimulation in vivo is the ratio of the tuned (F1) to the untuned postsynaptic ilar orientation preference as the postsynaptic neuron (and consequently response (F0) it evokes (refer to ref. 18, Fig. 4 A–D). We therefore modulated higher weights on average) were activated at higher rates, while synapses the firing rate of all synaptic inputs by a sine function of time to mimic an preferring the orthogonal orientation were activated at lower rates, and oscillating visual stimulus. We adjusted the scaling and offset of the sine vice versa (SI Appendix, Fig. S2C). Overall, synaptic input firing rates followed oscillation to match experimentally observed F0:F1 ratios (17, 18). All other a normal distribution with a mean of 7.5 Hz (3.75 Hz for nonpreferred) and SD synapses (“background synapses”) were active at a constant rate of 1.0 Hz of 4 Hz (2 Hz for nonpreferred). Distributed across synapses of different syn- (excitatory) or 6.0 Hz (inhibitory) (20, 21, 24, 28). Overall, the total time- aptic weights, this achieves the average synaptic firing rates described under In averaged excitatory and inhibitory synaptic conductance received by the vivo–like synaptic activation above. postsynaptic neuron during visual stimulation was consistent with the ex-

perimentally measured values (20). Implementation of Pharmacological Block of Nav Channels and NMDARs. To Synaptic weight distribution. The weights of excitatory signal synapses followed compare our model responses to pharmacological experiments (13, 17), we – a lognormal distribution (27 29, 31) (reference SI Appendix, Fig. S2B). We mimicked the block of Nav channels and NMDARs by setting gNa = 0or used the mean, median, and SD of the distribution of somatic EPSP ampli- freezing the voltage dependence of NMDARs at the resting potential, re-

tudes (in mV) recently measured by ref. 18 between pairs of L2/3 pyramidal spectively. For the Nav channel block, we applied gNa = 0 only to dendrites at neurons in mouse visual cortex (19, 109, 110) to fit a lognormal distribution a distance d > 50 μm from the soma to maintain the somatic resting mem- (SI Appendix, Fig. S2B, Top) with parameters μ = –1.51 and σ = 1.14 as the brane potential and AP threshold of the model. mean and SD of the underlying normal distribution, respectively. To translate the measured mean somatic EPSP amplitude into the peak AP-Triggered Averages of Dendritic Spikes. Detectors for dendritic Na+ spikes, conductance of a single synaptic contact (30), we simulated the activation of NMDA spikes, and bAPs are described in SI Appendix. We used STA to de- a single contact, determined the resulting somatic EPSP amplitude, and av- termine spatiotemporal windows during which dendritic Na+ spikes and eraged the results of iterating this procedure over all dendritic locations NMDA spikes can drive AP output. We found that windows relative to AP where the single active contact was placed (SI Appendix, Fig. S2A). We then onset from –15 to 0 ms for Na+ spikes and windows from –40 to 0 ms for adjusted the peak synaptic conductance of this single contact to match the NMDA spikes over the space of the whole dendritic tree were sufficient to experimentally measured somatic EPSP amplitude divided by the number of capture dendritic activity preceding somatic APs (Fig. 3D). We then used synaptic contacts per connection between L2/3 pyramidal neurons (2.8) (19, these windows to count the number of dendritic Na+ spikes and NMDA 105). We used a fixed number of synaptic contacts per connection for this spikes preceding a single AP. As a control, we counted dendritic Na+ spikes conversion since the correlation between the number of synaptic contacts and NMDA spikes in the same spatiotemporal windows placed at random per connection and the somatic EPSP amplitude is weak (19, 30), and other times during the visual response (see Fig. 3D). factors, such as dendritic location, presynaptic release probability, and post- synaptic conductance per synaptic contact are more important determinants Dendritic STAs of Synaptic Inputs. Analogous to the AP-triggered averages of of somatic EPSP amplitude. As this procedure assumes a release probability of dendritic spikes, we performed dendritic STAs of synaptic inputs. Here, we 1, it yields a conservative estimate of the conductance of an average synaptic found that spatiotemporal windows of −4 ms from the dendritic Na+ spike contact of 0.203 nS for excitatory signal synapses. initiation time and −1.5 ms from the NMDA spike initiation time, as well as Finally, we obtained the lognormal distribution of synaptic conductances 100 μm from the Na+ spike initiation site and NMDA spike initiation site, with this mean value (SI Appendix, Fig. S2B, Top) by linearly scaling the covered all synaptic inputs integrated by the dendritic spike (Fig. 5B). We

10 of 12 | PNAS Goetz et al. https://doi.org/10.1073/pnas.2017339118 Active dendrites enable strong but sparse inputs to determine orientation selectivity Downloaded by guest on October 1, 2021 used these windows to count the number of excitatory synaptic inputs that approximation to the charge delivered to the dendrite—the response is the can generate a local dendritic Na+ spike or NMDA spike, respectively. As a product of the synaptic strength and presynaptic firing rate, summed over control, we used the same spatiotemporal windows but triggered on per- all synapses. For synaptic inputs, dendritic Na+ spikes and NMDA spikes, as

muted spike initiation times while keeping the original spike initiation sites, well as somatic APs and Vm, we fitted a Gaussian to the orientation tuning taking into account the spatial and temporal statistics of spike initiation curve (117), which consisted of the number of events during 0°, 45°, 90°, and across the dendritic tree. The control values at random times are consistent 135° orientation for dendritic spikes and somatic APs, and the peak-to-

with a back-of-the-envelope calculation of the expected number of active trough amplitude of the cycle average for somatic Vm (17). synapses in the detection window for Na+ spikes (1.32 synapses/window) and NMDA spikes (0.49 synapses/window), taking into account the mean firing Removing Synapses. To “remove” n strong excitatory synapses from the in- rate (1.88 Hz) during the 200-ms peak in input firing, during which most APs put configuration in the preferred orientation, we first sorted all excitatory are triggered, mean synapse density on the dendritic tree (0.53 synapses/ synapses by descending synaptic weights and then set the firing rates of the 3 μm , see also refs. 115 and 116), as well as the spatial and temporal di- strongest n excitatory synapses to 0 Hz. In addition, we also set the rates of a 2 mensions of the detection window (332 μm dendritic surface area and 4 or matched number of randomly chosen inhibitory synapses to 0 Hz. To remove + 1.5 ms duration for Na spikes and NMDA spikes, respectively). n random excitatory synapses from the input configuration in the preferred orientation, we randomly selected n synaptic inputs and set their firing rates Measurement of Orientation Tuning. We used the OSI to determine orienta- to 0 Hz. Error bars show SD unless stated otherwise. tion tuning of synaptic input, dendritic spikes, somatic APs, and subthreshold membrane potential at the soma (VmOSI) (17). OSI is defined as follows: Data Availability. There are no data underlying this work. − = Rp Ro OSI + , ACKNOWLEDGMENTS. We thank Martine R. Groen for discussions and help Rp Ro with early simulations, Spencer Smith for providing data, Tiago Branco for providing an initial model, Christoph Schmidt-Hieber, Peter Jonas, and where Rp and Ro denote the response in the preferred and orthogonal di- Nelson Spruston for discussions, and Alex Bardon, Brendan Bicknell, Mehmet “ ” rection, respectively. We define OSI tuned, shown in Fig. 6 A, B, and D,as Fisek, Dustin Herrmann, and Peter Latham for their comments on the the OSI including only events that display orientation tuning, that is, where manuscript. This work was supported by grants from the , the difference between a fitted Gaussian and the data are less than 15% European Research Council (AdG 695709 DendriteCircuits) and a Boehringer of the peak response value (17). For the subthreshold dendritic response—an Ingelheim Fonds Fellowship to L.G.

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